Michigan State University was propelled on Thursday to the center of the sexual abuse scandal involving Dr. Lawrence G. Nassar, as state and federal agencies mounted investigations demanding to know what the college knew of his behavior and when.

Neither the sentencing of Dr. Nassar on Wednesday to 40 to 175 years in prison, nor the resignation of the university president a few hours later, quelled the furor. Education Secretary Betsy DeVos said on Thursday that her department would investigate Michigan State’s role, while state legislators asked that the university provide unredacted records of its investigations of Dr. Nassar and threatened to issue subpoenas if the school did not swiftly comply.

At the same time, the state attorney general was preparing his own review of the university, a United States senator asked for congressional hearings, and the speaker of the Michigan House called for the resignations of the university’s trustees, who are elected by voters.

“This is one of the biggest scandals in the history of our state,” said the speaker, Tom Leonard, a Republican, who has asked House lawyers to review options for removing trustees if they did not quit. “We are dealing with a Big Ten university. We are dealing with a monster who was a serial child molester and rapist who may have violated more victims than any other rapist in the history of our state.”

The repercussions were not limited to Michigan State. The head of the United States Olympic Committee, Scott Blackmun, wrote an email to U.S.A. Gymnastics, threatening to decertify the federation if its entire board did not resign by next Wednesday. Several board members, including the chairman, Paul Parilla, have already resigned.

Responding to Mr. Blackmun late Thursday, U.S.A. Gymnastics, the sport’s governing body, said it “completely embraces the requirements” outlined in the letter. The organization’s unsigned reply said U.S.A. Gymnastics would “work with the U.S.O.C. to accomplish change for the betterment of our organization, our athletes and our clubs.”

At Michigan State, university officials are already facing the prospect of legal judgments and fees from lawsuits filed by dozens of victims. At Penn State, where a former football coach was found to be a serial child molester, those costs have reached nearly a quarter of a billion dollars.

The lawsuits and the legislative inquiries center on what Michigan State knew about Dr. Nassar’s behavior during the two decades he worked there. Several victims have alleged that they had told Michigan State employees, as far back as the late 1990s, about being molested under the guise of treatment.

In 2014, after a complaint from a patient, the university conducted an internal investigation that cleared him, after which he continued to prey on more patients. On Thursday, ESPN reported that Michigan State had neglected to tell federal authorities, who were investigating the college’s handling of other sexual misconduct complaints, about the 2014 case until the accusations against Dr. Nassar became widely known in 2016.

“I feel like every day we are peeling back another layer of a very deep mystery,” said State Representative Adam Zemke, a Democrat who introduced a resolution that passed by a wide margin on Wednesday and called for the resignation of the university president, Lou Anna K. Simon. Hours later, she resigned.

Mr. Zemke said he saw parallels between what happened at Michigan State and the “willful negligence” during the water crisis in Flint, for which government officials have been charged with felonies and accused of covering up evidence.

In her resignation message, Ms. Simon wrote, “To the survivors, I can never say enough that I am so sorry that a trusted, renowned physician was really such an evil, evil person.”

She added: “As tragedies are politicized, blame is inevitable. As president, it is only natural that I am the focus of this anger.”

The Legislature’s deepening interest reflects the importance of Michigan State to the state and the realization that the scandal can easily become a political liability if not handled correctly. It has also become a subplot in this year’s race for governor. Among those who have had a role in the investigations are two candidates — the Republican attorney general, Bill Schuette, whose office prosecuted the state criminal cases, and a Democrat, Gretchen Whitmer, who was the county prosecutor in Lansing during part of the time that Dr. Nassar was being investigated.

Both Mr. Schuette and Ms. Whitmer have faced criticism by some for their work on the case, and both have strongly defended their record.

When The Detroit News wrote in an editorial this month that Mr. Schuette’s “indifference borders on dereliction of duty,” he called for a retraction and said “nothing could be further from the truth.” And after a foe in the Democratic primary race suggested Ms. Whitmer did not act aggressively enough on the case, she said that she was “proud of my record” and that “this is an issue that is incredibly close to my heart.”

“I think the system worked the way that it’s supposed to,” Ms. Whitmer said of the prosecution in an interview on Thursday. She also called for “a housecleaning” in Michigan State’s administration.

Jason Cody, a spokesman for the university, noted that its trustees had asked the state attorney general to investigate, and Mr. Cody said that the school would fully cooperate. The university has created a fund to help survivors get counseling and mental health services, he said.

“Many at M.S.U. viewed the brave women who came forward to tell their stories at Nassar’s sentencing hearing,” Mr. Cody said. “Words cannot express the sorrow we feel for Nassar’s victims; the thoughts and prayers of the entire M.S.U. community are with these women as we listen to their heartbreaking testimony.”

Dr. Nassar, 54, was sentenced on Wednesday for sexually abusing seven girls, though he had been accused by many more. His seven-day sentencing hearing drew more than 150 women, including Olympic gymnasts who are household names, to give wrenching testimony about what he had done to them.

Dozens of women, including gymnasts, swimmers, figure skaters, runners and basketball players, are now suing Dr. Nassar, Michigan State and U.S.A. Gymnastics, alleging abuse going back two decades. In court papers, they have said that they trusted Dr. Nassar because he was a renowned sports doctor, and the team physician for the United States gymnastics team.

Some of his patients said they complained to Michigan State employees, including the women’s gymnastics coach at the time, Kathie Klages, in the late 1990s, according to court papers, but were met with disbelief. A lawyer for Ms. Klages has not commented on the allegations.

In 2014, a recent graduate filed a complaint against Dr. Nassar under Title IX, the federal law governing sexual harassment and assault on campus. She said that she had sought out Dr. Nassar for hip pain, and that he molested her and became sexually aroused until she removed his hands from her body, according to court papers in the civil cases filed against him.

But after consulting with other medical professionals, including Dr. Nassar’s colleagues, the university’s investigation concluded that his treatment had been “medically appropriate,” the court papers said.

The abuse continued until 2016, when Rachael Denhollander, a former gymnast, told her story to The Indianapolis Star, and a police investigation soon began.

On Thursday, ESPN reported that Michigan State had failed to turn over its file on Dr. Nassar in 2014, when the Education Department was investigating unrelated complaints about the way the university had handled sexual assault and harassment cases. The university began turning over records in late 2016, ESPN reported, saying that the failure had been an oversight.

On Thursday, the education secretary said her agency would review Michigan State’s handling of the complaints against Dr. Nassar. “What happened at Michigan State is abhorrent,” Ms. DeVos said. “Students must be safe and protected on our nation’s campuses. The department is investigating this matter and will hold M.S.U. accountable for any violations of federal law.”

But in a December letter to Mr. Schuette, the Michigan attorney general, the university’s lawyer, Patrick Fitzgerald, said he believed that evidence would show that no Michigan State official believed that Dr. Nassar committed sexual abuse before the newspaper reports in 2016. The university is also arguing that it cannot be held liable because of Michigan’s sovereign immunity law, which protects state agencies from lawsuits in most circumstances and “protects the state’s citizens by safeguarding its fiscal stability,” the school said in a court filing.

John Manly, a lawyer for some of the women in the civil cases, said the university’s response to the lawsuits reminded him of the way the Roman Catholic Church had responded to allegations of child sex abuse by priests. “It’s a page right out of the bishops’ playbooks,” he said.

If Michigan State is ruled to be not immune, the cost could be significant. One state representative, Klint Kesto, a Republican, said he has drafted legislation that would prevent state funds from being used for payouts. If that bill is passed, it would force Michigan State to use tuition or endowment money. “The school should use all its assets, all its income from other sources first before they go into the pockets of taxpayers,” Mr. Kesto said.

On Thursday, Senator Gary Peters, a Democrat, called for congressional oversight and investigations of the scandal and said in a statement that it was “time for us to find out who is responsible at Michigan State University and U.S.A. Gymnastics for enabling and failing to stop this criminal.”

State legislators requested that university trustees provide investigative documents about Dr. Nassar dating back to 2014.

“It is our sincere hope that the university will cooperate with our request and inquiries without the need to employ means of compulsion,” the lawmakers wrote, adding that they may issue subpoenas if the records were not received by 5 p.m. on Feb. 9.